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College Math SECTION 3.2: TRUTH TABLES FOR NEGATION, CONJUNCTION, AND DISJUNCTION
Truth Tables ,[object Object],[object Object]
Truth Table for Negation ,[object Object],[object Object],P T T F F ~P Case 1 Case 2
Four Possible Cases ,[object Object],T T T T F F F F P Q Case 1 Case 2 Case 3 Case 4
When is a Conjunction True? ,[object Object],[object Object],[object Object]
When is a Conjunction True? cont’d. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Truth Table for Conjunction T T F F T F T F T F F F P Λ Q P Q Case 1 Case 2 Case 3 Case 4
3.2 Question 1 ,[object Object],[object Object]
When is Disjunction True? ,[object Object],[object Object],[object Object]
When is Disjunction True? cont’d. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Truth Table for Disjunction T T F F T F T F T T T F P V Q P Q Case 1 Case 2 Case 3 Case 4
3.2 Question 2 ,[object Object],[object Object]
Truth Table Summary ,[object Object],[object Object],[object Object],[object Object],[object Object]
Making a Truth Table Example ,[object Object],[object Object]
Truth Table for ~P V Q T T F F T F T F P ~P Q Q Opposite of Column 1 F F T T Same as Column 2 T F T F T F T T Final Answer column V
Another Example: P Λ ~Q T T F F T F T F P P Q ~Q Same as Column 1 T T F F Opposite of Column 2 F T F T F T F F Final Answer column Λ
3.2 Question 3 ,[object Object],[object Object],[object Object],[object Object],[object Object]
~P Λ ~Q Stop Day 1 T T F F T F T F P ~P Q ~Q Opposite of Column 1 F F T T Opposite of Column 2 F T F T F F F T Final Answer column Λ
More Complicated Truth Tables ,[object Object],[object Object],[object Object],[object Object],[object Object]
More Complicated Truth Tables Final Answer T T F F Opposite of Column 1 Opposite of Column 2 Same as Column 2 Same as Column 1 F T F T OR T T F T F F T T T F T F AND F F T F T T T T
More Complicated Truth Tables ,[object Object],[object Object],[object Object],[object Object]
More Complicated Truth Tables Final Answer T T F F Opposite of Column 1 Opposite of Column 2 Same as Column 2 Same as Column 1 F T F T OR T T F T F F T T T F T F AND F F T F F F F F P Q ( P ~Q ) ( ~P Q ) T T T F F T F F
Constructing Truth Tables with Three Simple Statements ,[object Object],P Q Case 1 T T Case 2 T F Case 3 F T Case 4 F F
Constructing Truth Tables with Three Simple Statements cont’d. ,[object Object]
Constructing Truth Tables with Three Simple Statements cont’d. P Q R Case 1 T T T Case 2 T T F Case 3 T F T Case 4 T F F Case 5 F T T Case 6 F T F Case 7 F F T Case 8 F F F
A Three Statement Example ,[object Object],[object Object]
A Three Statement Example T T T T F F F F T T F F T T F F F T F T F T F T T T T T T T F F F T F T F T F F P Q R (P Q) ~R T T T T T F T F T T F F F T T F T F F F T F F F Final Answer
Practice ,[object Object],[object Object],[object Object]
Practice ,[object Object],[object Object]
Practice ,[object Object]
DeMorgans Law (this guy again?)
More Complicated Truths; Quantifiers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Negations of Quantifiers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Examples of Negations with quantifiers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Truth tables

  • 1. College Math SECTION 3.2: TRUTH TABLES FOR NEGATION, CONJUNCTION, AND DISJUNCTION
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  • 7. Truth Table for Conjunction T T F F T F T F T F F F P Λ Q P Q Case 1 Case 2 Case 3 Case 4
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  • 11. Truth Table for Disjunction T T F F T F T F T T T F P V Q P Q Case 1 Case 2 Case 3 Case 4
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  • 15. Truth Table for ~P V Q T T F F T F T F P ~P Q Q Opposite of Column 1 F F T T Same as Column 2 T F T F T F T T Final Answer column V
  • 16. Another Example: P Λ ~Q T T F F T F T F P P Q ~Q Same as Column 1 T T F F Opposite of Column 2 F T F T F T F F Final Answer column Λ
  • 17.
  • 18. ~P Λ ~Q Stop Day 1 T T F F T F T F P ~P Q ~Q Opposite of Column 1 F F T T Opposite of Column 2 F T F T F F F T Final Answer column Λ
  • 19.
  • 20. More Complicated Truth Tables Final Answer T T F F Opposite of Column 1 Opposite of Column 2 Same as Column 2 Same as Column 1 F T F T OR T T F T F F T T T F T F AND F F T F T T T T
  • 21.
  • 22. More Complicated Truth Tables Final Answer T T F F Opposite of Column 1 Opposite of Column 2 Same as Column 2 Same as Column 1 F T F T OR T T F T F F T T T F T F AND F F T F F F F F P Q ( P ~Q ) ( ~P Q ) T T T F F T F F
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  • 25. Constructing Truth Tables with Three Simple Statements cont’d. P Q R Case 1 T T T Case 2 T T F Case 3 T F T Case 4 T F F Case 5 F T T Case 6 F T F Case 7 F F T Case 8 F F F
  • 26.
  • 27. A Three Statement Example T T T T F F F F T T F F T T F F F T F T F T F T T T T T T T F F F T F T F T F F P Q R (P Q) ~R T T T T T F T F T T F F F T T F T F F F T F F F Final Answer
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  • 31. DeMorgans Law (this guy again?)
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